Let g(x) = x – 3x3. %D (a) Determine the critical points of g(x).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let g(x) = x -
x – 3x³.
(a)
Determine the critical points of g(x).
(b)
Use the Second Derivative Test to verify that these points are local extrema. If the Second Derivative Test fails, say so.
(c)
Determine any points of inflection for g(x).
Transcribed Image Text:Let g(x) = x - x – 3x³. (a) Determine the critical points of g(x). (b) Use the Second Derivative Test to verify that these points are local extrema. If the Second Derivative Test fails, say so. (c) Determine any points of inflection for g(x).
Expert Solution
Step 1

The given function is:

Calculus homework question answer, step 1, image 1

Differentiating g(x) with respect to x we get,

 

Calculus homework question answer, step 1, image 2

Calculus homework question answer, step 1, image 3

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